【摘要】 讨论分段连续型微分方程x′(t)=ax(t)+a1x([t+3])的解析解的稳定性,得出其渐进稳定的一个充分必要条件。应用θ-方法求解此分段连续型微分方程,得到相应的数值稳定区域,给出数值解的稳定区域包含解析解的稳定区域的一个充分必要条件。应用线性θ-方法求解了微分方程x′(t)=ax(t)+a1x([t+p]),给出此类数值方法渐进稳定的一个充分条件,得出数值解的稳定区域包含解析解的稳定区域的充分条件。更多还原

【Abstract】 The stability of the analytic solution of the differential equation x′(t)=ax(t)+a1x() with piecewise continuous arguments is considered.The conditions of asymptotic stability for the equation are obtained.Moreover,θ-methods are applied to this kind of equations,and the stability region of θ-method is obtained.A necessary and sufficient condition under which the analytic stability region is contained in the numerical stability region is also obtained.Then,apply the linear θ-method to the equation x′(t)=ax(t)+a1x(),a sufficient condition of the asymptotic stability is investigated,and a sufficient condition is obtained under which the analytic stability region is contained in the numerical stability region.更多还原